Do not think you need a spot welder. Just apply solder paste to the IC pads, do the pick-and-place, then carefully put in an oven for reflow. If parts need to go on other side, make sure all small parts get reflowed on one side first, leaving the side with bigger parts ("squashed bugs" i call them) on top when reflow. The capillary action of the (liquid) solder on the "bottom" side is more than strong enough tohold small parts. I have a board that holds about 78 parts on both sides; the PCB is
0.5 by 1.4 including pads for wires. The only problems i have seen was due to one lead not being wetted during fab.